weiss2010d

However, we need the inverse mapping to detect which positions on the GUI are touched. Our algorithm computes the map C∗ j by uniformly evaluating the patch P with a high sampling rate. For each sample, the source GUI position is stored at the target camera position in C∗j . This yields a discrete inverse map for camera j. Afterwards, if a spot is visible in camera j, we can read its GUI position from C∗j . In order to avoid jitter, we employ bilinear interpolation for this lookup.

Although the calibration involves manual user interaction, it does not require more than five minutes in practice. Furthermore, it only has to be repeated when the camera setup is changed. In our case, a 20 × 20 grid was sufficient to calibrate all cameras.

EVALUATION Dragging is a simple and one of the most frequently used gestures on interactive tabletops. However, dragging performance on curved surfaces is still a mostly unexplored topic. In this section, we present several user tests that investigate the dragging performance on the different areas of the table. We furthermore test the virtual aiming across curved surfaces, which is, e.g., important for flinging gestures.

Participants A total of 18 participants (16 males), aged between 24 and 32 years (mean age 27 years) took part in the study. They did not receive any compensation, but we raffled a $25 gift coupon among them. 15 participants were computer scientists, two were school teachers, and one was a mechanical engineer.

Generalprocedure The study was carried out in a dimly lit room, where participants sat in front of the BendDesk. Participants worked throughout three different interaction tasks: two dragging tasks and a virtual aiming task. Each task type was introduced by a test trial to familiarize participants with the new task. The task instructions were standardized and it was emphasized to solve the tasks as fast and accurate as possible. In total the experiment lasted about 40 to 60 minutes.

Dragging across the curve We first investigated dragging performance across the different interactive areas of BendDesk and compared dragging performance across the curve to dragging on the planar board and tabletop area.

Task design and procedure The experimental task and the conditions are depicted in Figure 4. The system displayed the source, a white colored square with a side length of 50 px (4.8 cm), and the target, a white frame of the same size. Both were vertically arranged with a distance of 150 px (14.64 cm). The participant had to drag the source quad onto the target using her index finger. After successfully matching source and target (we allowed a tolerance of 10 px, or 0.98

ITS 2010: Displays November 7-10, 2010, Saarbrucken, Germany

(1) horizontal

(2) curve

(3) vertical upwards downwards area

Figure 4: Experimental design of vertical dragging task.

cm), the interactive area went blank and the next trial was displayed. They appeared in three different areas (in the horizontal plane, the curve, or the vertical plane), and dragging direction from source to target was either upwards or downwards. This resulted in 3 (area) × 2 (dragging direction) experimental conditions. We further controlled the distribution of trials across the surface by presenting trials on seven different x-positions with two repetitions each. The order of trials was randomized. Participants worked throughout 84 trials with their dominant hand and throughout another 84 trials with their non-dominant hand. This yielded a total number of 168 dragging operations per participant. Dragging duration was defined as the interval from touching the source until correctly releasing it when the source was placed in the target (given in ms). Dragging trajectory covered the observed length of the finger’s movement path, again from touching the source until correctly releasing it when the source was placed in the target (given in px).

We hypothesized the following outcomes:

• H1 (horizontal vs. vertical): Dragging (a) duration and (b) trajectory are shorter on the horizontal surface than on the vertical one.

Results The data were analyzed for each of the dependent variables with 3 × 2 analyses of variances (ANOVAs) with the within-subject factors area and direction. Dragging durations are depicted in Figure 5. The ANOVA revealed a significant main effect of the factor area (F(2,34) = 14.20;p < 0.01). Dragging durations inside the curve (mean 16 ms) were 14% (150 ms) longer than the dragging durations on horizontal curve vertical

Figure 6: Length of dragging trajectory depending on area and direction.

the horizontal area (mean 1016 ms) and 10% (110 ms) longer than the dragging durations on the vertical area (mean 1056 ms). Other main effects and the interaction were not significant.

Figure 6 illustrates the length of dragging trajectories. The ANOVA showed a significant main effect of the factor area (F(2,34) = 28.84;p < 0.01). The dragging trajectories inside the curve (mean 167 px) were 3% (5 px) longer than the dragging trajectories on the horizontal area (mean 162 px). But dragging through the curve was equally long compared to vertical dragging (mean 168 px). Furthermore, for the horizontal plane, but not for the other areas, upward dragging was significantly shorter than downward dragging. This yielded a significant interaction (F(2,34) = 4.73;p < 0.05). The main effect of the factor direction alone was not significant.

To sum up, when comparing horizontal and vertical dragging (H1) the results clearly showed shorter trajectories for operations in the horizontal plane. This is in accordance with H1. However, dragging duration was comparable for both planes. On a first glance this is not further surprising, since finger amplitude and target size remained constant over the task. So, in accordance with Fitts’ Law [9], movement durations should be constant as well. However, on a second glance the results also show that the movement plane seemed to have no

further effect on movement durations. The main finding is, that movement execution was optimized along the observed movement path. This optimization did not lead to any further improvement of movement duration, probably caused by a bottom effect—durations were very short and seemed to be already at a minimum for the given distance. Second, our results support H2: dragging on a planar surface is indeed more efficient (in terms of durations) than dragging across the curve. Concerning Fitts’ Law [9] this is a rather unexpected finding, as with a constant index of difficulty one would have expected constant movement durations over all areas. As this is clearly not the case findings suggest that motor control across the curve is more complex and therefore takes longer. Considering the movement path, only horizontal but not vertical dragging was superior to dragging in the curved area. This might indicate that motor control is more difficult for dragging in a curved or vertical area than in the horizontal area. Finally, we hypothesized more efficient upward than downward movements (H3). Although performance data in both planar surfaces slightly hint at an advantage for upward movements, this was only significant for horizontal finger trajectories. Thus, overall the data did not confirm H3.

Cross-dragging performance depending on angle

With the second task we explored dragging performance not within an area (as in Task 1) but across the whole BendDesk surface and we compared if dragging performance depended on the angle of approach.

Task design and procedure The experimental task is depicted in Figure 7. Our system displayed the source, a white colored circle and the target, a black colored circle inside a white ring. Both circles had a diameter of 60 px (5.82 cm) and the thickness of the target ring amounts to 20 px (1.94 cm). The distance between source and target was 600 px (58.20 cm). As in Task 1, participants had to drag the source onto the target using the index finger. After successfully matching source and target (within a tolerance of 10 px,

Figure 8: Length of dragging trajectory depending on angle.

or 0.98 cm), the interactive area went blank and the next trial appeared.

Trials appeared in 9 different movement directions (with two repetitions each): (1) 45◦, (2) 35◦, (3) 25◦, (4) 15◦ to the left, (5) 0◦ (vertical line), and (6) 15◦, (7) 25◦, (8) 35◦, (9) 45◦ to the right. The movement started either in the horizontal area (upward) or the vertical area (downward). The order of trials was randomized. Participants worked throughout 36 trials with their dominant hand and throughout another 36 trials with their non-dominant hand. A total of 72 dragging operations were presented. Dependent variables were the same as described in Task 1.

We assumed that a larger angle yields a lower dragging performance and higher deviation from the ideal dragging line:

Results Data were analyzed for each of the dependent variables with one-factorial analyses of variances (ANOVAs) with the within-subject factors angle. For dragging durations the ANOVA revealed a significant main effect for the factor angle (F(8,128) = 2.65;p < 0.05). Dragging durations varied between 1306 and 3806 ms. However, the differences across angles were too small to show statistical significance in post-hoc comparisons.

The mean length of dragging trajectories are depicted in Figure 8. We found a significant main effect of the factor angle (F(8,128) = 8.94;p < 0.01). Post-hoc comparison showed that dragging trajectories for targets 45◦ to the left or to the right of the source (mean 652 px) were significantly longer when compared to targets vertically presented to the source (mean 631 px).

Furthermore, deviation of movement trajectories from the direct connection between source and target were analyzed (Figure 9 and Figure 10). The ANOVA showed significant main effects of the factor angle for the maximum (F(8,128) = 1.6;p < 0.01) as well as the average (F(8,128) = 10.51;

ITS 2010: Displays November 7-10, 2010, Saarbrucken, Germany

Figure 9: Dragging trajectories for upward dragging across the curve for different angles. Variance significantly increases with higher angles.

Figure 10: Average deviation from direct line between source and target depending on angle.